The $K$-theoretic bulk-edge correspondence for topological insulators

Abstract

We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real $C^{\ast }$-algebras and $KKO$-theory must be used.

Minor corrections, to appear in Annales Henri Poincaré

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Cited by in corpus (35)

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• Bulk-boundary correspondence for disordered free-fermion topological phases
• Microlocal analysis of the bulk-edge correspondence
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• Finite volume calculation of $K$-theory invariants
• The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
• The Bulk-Edge Correspondence in Three Simple Cases
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
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